Equivalence of Regularization and Truncated Iteration for General Ill-Posed Problems

Linear Algebra and Its Applications

Volumn 236, Issue , 1996, Pages 25-33

  Santos, Reginaldo J ^a,b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030546173     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/0024-3795(94)00114-6     Document Type: Article

References (12)

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2. S. L. Campbell and C. D. Meyer, Jr., Generalized Inverses of Linear Transformations, Pitman, San Francisco, 1979.
3. A. Dax, The convergence of linear stationary iterative processes for solving singular unstructured system of linear equations, SIAM Rev. 32(4):611-635 (1990).
4. H. E. Fleming, Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems, Linear Algebra Appl. 130:133-150 (1990).
5. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins U.P., Baltimore, 1989.
6. C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind, Pitman, Boston, 1984.
7. M. Hanke and P. C. Hansen, Regularization methods for large-scale problems, Surveys Math. Indust. 3:253-315 (1993).
8. L. Landweber, An iteration formula for Fredholm integral equations of the first kind, Amer. J. Math. 73:615-624 (1951).
9. O. N. Strand, Theory and methods related to the singular-function expansion and Landweber's iteration for integral equations of the first kind, SIAM J. Numer. Anal. 11:798-825 (1974).
10. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems, Wiley, New York, 1977.
11. G. Wahba, Three topics in ill-posed problems, in Inverse and Ill-Posed Problems (H. Engl and C. Groetsch, Eds.), Academic, New York, 1987.
12. D. M. Young, Iterative Solutions of Large Linear Systems, Academic, New York, 1971.